期刊
ADVANCES IN MATHEMATICS
卷 333, 期 -, 页码 796-821出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2018.05.038
关键词
Schrodinger equation; Dispersive estimates; Jacobi polynomials
类别
资金
- Austrian Science Fund (FWF) [P26060]
- Austrian Science Fund (FWF) [P26060] Funding Source: Austrian Science Fund (FWF)
The present paper is about Bernstein-type estimates for Jacobi polynomials and their applications to various branches in mathematics. This is an old topic but we want to add a new wrinkle by establishing some intriguing connections with dispersive estimates for a certain class of Schrodinger equations whose Hamiltonian is given by the generalized Laguerre operator. More precisely, we show that dispersive estimates for the Schrodinger equation associated with the generalized Laguerre operator are connected with Bernstein type inequalities for Jacobi polynomials. We use known uniform estimates for Jacobi polynomials to establish some new dispersive estimates. In turn, the optimal dispersive decay estimates lead to new Bernstein-type inequalities. (C) 2018 Elsevier Inc. All rights reserved.
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